Inversion polynomials for 321-avoiding permutations
نویسندگان
چکیده
منابع مشابه
Inversion polynomials for 321-avoiding permutations
We prove a generalization of a conjecture of Dokos, Dwyer, Johnson, Sagan, and Selsor giving a recursion for the inversion polynomial of 321-avoiding permutations. We also answer a question they posed about finding a recursive formulas for the major index polynomial of 321-avoiding permutations. Other properties of these polynomials are investigated as well. Our tools include Dyck and 2-Motzkin...
متن کاملInversion polynomials for 321-avoiding permutations: addendum
This addendum contains results about the inversion number and major index polynomials for permutations avoiding 321 which did not fit well into the original paper. In particular, we consider symmetry, unimodality, behavior modulo 2, and signed enumeration.
متن کاملInversion Formulae on Permutations Avoiding 321
We will study the inversion statistic of 321-avoiding permutations, and obtain that the number of 321-avoiding permutations on [n] with m inversions is given by
متن کامل321-Polygon-Avoiding Permutations and Chebyshev Polynomials
A 321-k-gon-avoiding permutation π avoids 321 and the following four patterns: k(k + 2)(k + 3) · · · (2k − 1)1(2k)23 · · · (k − 1)(k + 1), k(k + 2)(k + 3) · · · (2k − 1)(2k)12 · · · (k − 1)(k + 1), (k + 1)(k + 2)(k + 3) · · · (2k − 1)1(2k)23 · · · k, (k + 1)(k + 2)(k + 3) · · · (2k − 1)(2k)123 · · · k. The 321-4-gon-avoiding permutations were introduced and studied by Billey and Warrington [BW]...
متن کاملKazhdan-Lusztig Polynomials for 321-Hexagon-Avoiding Permutations
In (Deodhar, Geom. Dedicata, 36(1) (1990), 95–119), Deodhar proposes a combinatorial framework for determining the Kazhdan-Lusztig polynomials Px,w in the case where W is any Coxeter group. We explicitly describe the combinatorics in the case where W = Sn (the symmetric group on n letters) and the permutation w is 321-hexagon-avoiding. Our formula can be expressed in terms of a simple statistic...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2013
ISSN: 0012-365X
DOI: 10.1016/j.disc.2013.07.026